Recall that a ring is reduced if it has no nonzero nilpotent elements. Lambek [1]}, called a ring \(R\)  symmetric if \(abc=0\)  implies \(acb=0\)  for \(a,b,c\in R\) . Every reduced ring is symmetric ([2]}) but the converse does not hold by [3]}. Cohen [4]}, called a ring \(R\)  reversible if \(ab=0\)  implies \(ba=0\)  for \(a,b\in R\) . It is obvious that commutative rings are symmetric and symmetric rings are reversible, but the converse does not hold by [3]} and [6]}. From [7]}, a ring \(R\)  is called right \((\) left\()\)  \(\sigma \) -reversible if whenever \(ab=\)  for \(a,b\in R\) , \(b\sigma (a)=0\)  (\(\sigma (b)a=0\) ). \(R\)  is called \(\sigma \) -reversible if it is both right and left \(\sigma \) -reversible. Also, by [8]}, a ring \(R\)  is called right \((\) left\()\)  \(\sigma \) -symmetric if whenever \(abc=0\)  for \(a, b, c \in R\) , \(ac\sigma (b)=0\)  (\(\sigma (b)ac=0\) ). \(R\)  is called \(\sigma \) -symmetric if it is both right and left \(\sigma \) -symmetric. Clearly right \(\sigma \) -symmetric rings are right \(\sigma \) -reversible.
